Conditional extreme risk,black swan hedging,and asset prices

Motivated by the asset pricing theory with safety-first preference, we introduce and operationalize a conditional extreme risk (CER) measure to describe expected stock performance conditional on a small-probability market downturn (black swan). We document a significant CER premium in the cross-section of expected returns. We also demonstrate that CER explains the premia to downside beta, coskewness, and cokurtosis. CER provides distinct information regarding black swan hedging that cannot be captured by co-crash-based tail dependence measures. As we find that the pricing effect is stronger among black swan hedging stocks, this distinction helps explain the absence of premium to tail dependence.     

Backtesting extreme value theory models of expected shortfall

We use stock market data to analyze the quality of alternative models and procedures for forecasting expected shortfall (ES) at different significance levels. We compute ES forecasts from conditional models applied to the full distribution of returns as well as from models that focus on tail events using extreme value theory (EVT). We also apply the semiparametric filtered historical simulation (FHS) approach to ES forecasting to obtain 10-day ES forecasts. At the 10-day horizon we combine FHS with EVT. The performance of the different models is assessed using six different ES backtests recently proposed in the literature. Our results suggest that conditional EVT-based models produce more accurate 1-day and 10-day ES forecasts than do non-EVT based models. Under either approach, asymmetric probability distributions for return innovations tend to produce better forecasts. Incorporating EVT in parametric or semiparametric approaches also improves ES forecasting performance. These qualitative results are also valid for the recent crisis period, even though all models then underestimate the level of risk. FHS narrows the range of numerical forecasts obtained from alternative models, thereby reducing model risk. Combining EVT and FHS seems to be best approach for obtaining accurate ES forecasts.     

Measuring systemic importance of financial institutions: An extreme value theory approach

This paper proposes a set of market-based measures on the systemic importance of a financial institution or a group of financial institutions, each designed to capture different aspects of systemic importance of financial institutions. Multivariate extreme value theory approach is used to estimate these measures. Using six big Canadian banks as the proxy for Canadian banking sector, we apply these measures to identify systemically important banks in Canadian banking sector and major risk contributors from international financial institutions to Canadian banking sector. The empirical evidence reveals that (i) the top three banks, RBC Financial Group, TD Bank Financial Group, and Scotiabank, are more systemically important than other banks, while we also find that the size of a financial institution should not be considered as a proxy of systemic importance; (ii) compared to the European and Asian banks, the crashes of the U.S. banks, on average, are the most damaging to Canadian banking sector, while the risk contribution to the Canadian banking sector from Asian banks is quite lower than that from banks in the U.S. and euro area; (iii) the risk contribution to Canadian banking sector exhibits “home bias”, that is, cross-country risk contribution tends to be smaller than domestic risk contribution.     

Portfolio selection: An extreme value approach

We show theoretically that lower tail dependence (χ), a measure of the probability that a portfolio will suffer large losses given that the market does, contains important information for risk-averse investors. We then estimate χ for a sample of DJIA stocks and show that it differs systematically from other risk measures including variance, semi-variance, skewness, kurtosis, beta, and coskewness. In out-of-sample tests, portfolios constructed to have low values of χ outperform the market index, the mean return of the stocks in our sample, and portfolios with high values of χ. Our results indicate that χ is conceptually important for risk-averse investors, differs substantially from other risk measures, and provides useful information for portfolio selection.     

Managing extreme risks in tranquil and volatile markets using conditional extreme value theory

Financial risk management typically deals with low-probability events in the tails of asset price distributions. To capture the behavior of these tails, one should therefore rely on models that explicitly focus on the tails. Extreme value theory (EVT)-based models do exactly that, and in this paper, we apply both unconditional and conditional EVT models to the management of extreme market risks in stock markets. We find conditional EVT models to give particularly accurate Value-at-Risk (VaR) measures, and a comparison with traditional (Generalized ARCH (GARCH)) approaches to calculate VaR demonstrates EVT as being the superior approach both for standard and more extreme VaR quantiles.     

Electricity spot price modelling with a view towards extreme spike risk

Sums of Lévy-driven Ornstein–Uhlenbeck processes are appropriate for modelling electricity spot price data. In this paper we present a new estimation method with particular emphasis on capturing the high peaks, which is one of the stylized features of such data. After introducing our method we show it at work for the EEX Phelix Base electricity price index. We also present a small simulation study to demonstrate the performance of our estimation procedure.     

Using extreme value theory to estimate the likelihood of banking sector failure

Abstract

The growing interest in management of credit risk and estimation of default probabilities has given rise to a range of more or less elaborate credit risk models. While these models work well for non-financial firms they are usually not very successful in capturing the financial strength of banks. As an answer to this, Hall and Miles suggest a simple approach of estimating bank failure probabilities based solely on their stock prices. This paper suggests an extension to the Hall and Miles model using extreme value theory and applies the extended model to the Swedish banking sector around the banking crisis of the early 1990s. The extended model captures very well the increased likelihood of a systemic banking sector failure around the peak of the crisis and it produces default probabilities that are more stable, more realistic and more consistent with Moody’s and Fitch rating implied default rates than probabilities from the original Hall and Miles model.     

Estimation of tail‐related risk measures in the Indian stock market: An extreme value approach

The purpose of the study is to estimate tail-related risk measures using extreme value theory (EVT) in the Indian stock market. The study employs a two stage approach of conditional EVT originally proposed by McNeil and Frey (2000) to estimate dynamic Value at Risk (VaR) and expected shortfall (ES). The dynamic risk measures have been estimated for different percentiles for negative and positive returns. The estimates of risk measures computed under different quantile levels exhibit strong stability across a range of the selected thresholds, implying the accuracy and reliability of the estimated quantile based risk measures.     

Corporate risk management and firm value: evidence from the UK market

The paper evaluates the effect of corporate risk management activities on firm value, using a sample of large UK non-financial firms. Following recent changes in financial reporting standards, we are able to collect detailed information on risk management activities from audited financial reports. This enables us to gain a better understanding of risk management practices and to investigate value implications of different types of hedging. Overall 86.88% of the firms in the sample use derivatives to manage at least one type of price risk. The hedging premium is statistically and economically significant for foreign currency derivative users, while we provide weak evidence that interest rate hedging increases firm value. The extent of hedging and the hedging horizon have an impact on the hedging premium, whereas operational risk management activities do not significantly influence the market value of the firm.     

Financial hedging with derivatives and its impact on the Colombian market value for listed companies

The financial theory (Modigliani & Miller, 1958) presents risk management as a matter without importance in companies, given that the shareholders themselves managed their hedges, diversifying their portfolios. However, subsequent studies dispute said premise and present evidence that business financial hedging improves performance and increases the value of the same (Ahmed, Azevedo, & Guney, 2014; Allayannis & Weston, 2001; Kapitsinas, 2008). The efficient market risk management is supported in the financial derivatives, and demands strategic and efficient administrators in hedges that add value, especially in the face of clashes and macroeconomic and financial imbalances. The empirical evidence analyzes the behavior of the Q-Tobin as an indicator of the effect of the hedge strategies for the exchange rate associated to the market value. The aim of this work is to find evidence in Colombia on the effect of the use of derivatives in the market value of the company. Its added value lies in the analysis that is done by economic sectors, identified by ISIC codes and grouped into five (5) macro sectors (Agriculture and livestock, Commercial, Industrial or Manufacture, Services, and Construction). The methodology used includes the estimation of several regression models in data panels, using a Pooled regression model with fixed and random effect estimators through the maximum likelihood estimator. In general, a statistical and financially significant premium for hedges was found for companies exposed to exchange rate risks that use derivatives of a 6.3% average on the market value. Additionally, mixed results were found in relation to the variables analyzed in the model.     

Stochastic dominance statistics for risk averters and risk seekers: an analysis of stock preferences for USA and China

Recent research has found a number of scaling law relationships in foreign exchange data. These relationships, estimated using simple ordinary least squares, can be used to forecast losses in foreign exchange time series from as little as one month’s tick data. We compare the loss forecasts from a new scaling law against six parametric Value at Risk models. Compared to these models, the new scaling law is easier to fit, provides more stable forecasts and is very accurate.     

Capturing downside risk in financial markets: the case of the Asian Crisis

Using data on Asian equity markets, we observe that during periods of financial turmoil, deviations from the mean-variance framework become more severe, resulting in periods with additional downside risk to investors. Current risk management techniques failing to take this additional downside risk into account will underestimate the true Value-at-Risk with greater severity during periods of financial turnoil. We provide a conditional approach to the Value-at-Risk methodology, known as conditional VaR-x, which to capture the time variation of non-normalities allows for additional tail fatness in the distribution of expected returns. These conditional VaR-x estimates are then compared to those based on the RiskMetrics™ methodology from J.P. Morgan, where we find that the model provides improved forecasts of the Value-at-Risk. We are therefore able to show that our conditional VaR-x estimates are better able to capture the nature of downside risk, particularly crucial in times of financial crises.     

Extreme observations and risk assessment in the equity markets of MENA region: Tail measures and Value-at-Risk

The standard “delta-normal” Value-at-Risk methodology requires that the underlying returns generating distribution for the security in question is normally distributed, with moments which can be estimated using historical data and are time-invariant. However, the stylized fact that returns are fat-tailed is likely to lead to under-prediction of both the size of extreme market movements and the frequency with which they occur. In this paper, we use the extreme value theory to analyze four emerging markets belonging to the MENA region (Egypt, Jordan, Morocco, and Turkey). We focus on the tails of the unconditional distribution of returns in each market and provide estimates of their tail index behavior. In the process, we find that the returns have significantly fatter tails than the normal distribution and therefore introduce the extreme value theory. We then estimate the maximum daily loss by computing the Value-at-Risk (VaR) in each market. Consistent with the results from other developing countries [see Gencay, R. and Selcuk, F., (2004). Extreme value theory and Value-at-Risk: relative performance in emerging markets. International Journal of Forecasting, 20, 287–303; Mendes, B., (2000). Computing robust risk measures in emerging equity markets using extreme value theory. Emerging Markets Quarterly, 4, 25–41; Silva, A. and Mendes, B., (2003). Value-at-Risk and extreme returns in Asian stock markets. International Journal of Business, 8, 17–40], generally, we find that the VaR estimates based on the tail index are higher than those based on a normal distribution for all markets, and therefore a proper risk assessment should not neglect the tail behavior in these markets, since that may lead to an improper evaluation of market risk. Our results should be useful to investors, bankers, and fund managers, whose success depends on the ability to forecast stock price movements in these markets and therefore build their portfolios based on these forecasts.     

Change analysis of a dynamic copula for measuring dependence in multivariate financial data

This paper proposes a new approach to measure dependencies in multivariate financial data. Data in finance and insurance often cover a long time period. Therefore, the economic factors may induce some changes within the dependence structure. Recently, two methods have been proposed using copulas to analyse such changes. The first approach investigates changes within the parameters of the copula. The second determines the sequence of copulas using moving windows. In this paper we take into account the non-stationarity of the data and analyse the impact of (1) time-varying parameters for a copula family, and (2) the sequence of copulas, on the computations of the VaR and ES measures. We propose tests based on conditional copulas and the goodness-of-fit to decide the type of change, and further give the corresponding change analysis. We illustrate our approach using the Standard & Poor 500 and Nasdaq indices in order to compute risk measures using the two previous methods.     

The extreme risk connectedness of the new financial system: European evidence

The paper empirically analyses the tail risk connectedness between FinTech and the banking sector in the European context over 2015–2022. For this purpose, we use the Tail-Event driven NETworks (TENET) risk model, i.e., we can capture the behaviour of extreme (negative and positive) risk spillover within the financial system. The results highlight how most tail risk spillovers are from banks to FinTech firms. Also, the findings suggest that the spillovers of cross-sector tail risk are more significant in downside (bearish) risk conditions than in upside (bullish) one. We find evidence of an asymmetric effect of extreme risk spillover to the real economy. Finally, we evaluate the monetary policy’s impact on extreme risk. Our findings highlight the importance of closer monitoring risk spillover between FinTech institutions and the European banking system to maintain financial stability.     

Two-step methods in VaR prediction and the importance of fat tails

This paper proposes a two-step methodology for Value-at-Risk prediction. The first step involves estimation of a GARCH model using quasi-maximum likelihood estimation and the second step uses model filtered returns with the skewed t distribution of Azzalini and Capitanio [J. R. Stat. Soc. B, 2003, 65, 367–389]. The predictive performance of this method is compared to the single-step joint estimation of the same data generating process, to the well-known GARCH-Evt model and to a comprehensive set of other market risk models. Backtesting results show that the proposed two-step method outperforms most benchmarks including the classical joint estimation method of same data generating process and it performs competitively with respect to the GARCH-Evt model. This paper recommends two robust models to risk managers of emerging market stock portfolios. Both models are estimated in two steps: the GJR-GARCH-Evt model and the two-step GARCH-St model proposed in this study.     

Testing for differences in the tails of stock-market returns

In this paper, we use a database consisting of daily stock-market returns for 20 countries to test for similarities between the left and right tails of returns, as well as across countries. We estimate and test using the distribution of extreme returns over subsamples approach. Via Monte-Carlo simulations, we show that maximum-likelihood estimators are essentially unbiased, provided the size of subsamples is correctly chosen, and that the likelihood-ratio tests on parameters characterizing the behavior of extremes are correctly sized. For actual returns, we find that left and right tails behave very similarly. Across countries, we find that extremes are located at different levels and that their dispersion varies. The tail index, characterizing large extreme realizations, is found to be constant within each geographical group. We verify that the perception that left tails are heavier than right ones is not due to clustering of extremes. The failure to detect statistical significant differences is likely to be due to the relative infrequency of large extremes.     

基于条件极值分布的金融高频数据VaR动态估计模型

高频数据由于自身数量大、周期短、信息丰富的特点而受到关注。基于高频数据。对金融时间序列的厚尾特征进行条件极值分布下的VaR估计。在对条件均值和条件波动率估计时,以往采用一阶自回归模型和GARCH模型,但基于高频数据的估计较为繁复。为了充分利用日内信息,基于高频样本观测值,建立已实现均值RM模型,在考虑市场异质性的基础上,对条件均值进行估计。通过对TCL股票价格进行实证分析,估计出VaR风险值,验证模型是合理的。     

Exchange rate risk exposure and the value of European firms

This paper presents a new assessment of the exposure of European firms to exchange rate fluctuations which takes into account the potential common drivers of exchange rates and equity market conditions. Using monthly data for European firms from 1999 to 2011, we assess the impact of unexpected fluctuations in the USD, JPY, GBP and CHF against the Euro, and show that the proportion of firms subject to exchange rate risk is considerably larger when estimation accounts for potential common drivers and firm-specific factors than otherwise. Firm exposure to exchange rate risk is affected by the level of international involvement, industry, firm size and country of origin. European firms with largely domestic operations reveal the greatest vulnerability to unexpected exchange rate movements, suggesting an opportunity to improve risk management for these companies.     

An analysis of real-estate risk using the present value model

The current study uses a present value model that allows for a time-varying expected discount rate in conjunction with a VAR process to decompose real-estate risk. The study finds that the variance ofunexpected returns accounts for most of the total risk with cash-flow risk accounting for twice as much of the unexplained real-estate risk although discount rate risk is also an important factor. This dominance of cash-flow risk is found to result in a weaker mean reversion process for real estate relative to stocks. Another finding is that real estate investors tend to become apprehensive about the future when news on future cash flow is good, and thus they demand higher expected future returns.